Pretty sure it would be 2 Right angles
12 I got it form Socratic
To solve this problem, let us say that:
money invested in stock A = A
money invested in stock B = B
money invested in stock C = C
The given problem states that:
C = A * (1 / 4) = 0.25 A
B = A * (1 / 2) = 0.50 A
It was stated that we only have $16,000 to invest.
Therefore:
A + B + C = 16,000
Substituting values of C and B in terms of A:
A + 0.50 A + 0.25 A = 16,000
1.75 A = 16,000
A = $9,142.86
So C and B is:
C = 0.25 (9142.86)
C = $2285.71
B = 0.50 (9142.86)
B = $4571.43
Answer:
The reason why this may be happening is because the expenses may be higher than the amount of revenue that the business is making, the cost of rent, paying the employees and running the business may be higher than the revenue that is being made. The inflows may be higher than the outflows, in which case the profit is lower than the loss and may be the reason why the owner is having trouble keeping the business running.
Answer:
x-y-3=0
Step-by-step explanation:
Choose two common points on the line of intersection of the planes x − z = 3 and y + 2z = 3:
- 1st point: if x=0, then z=-3 and y=3-2z=3+6=9, so the 1st point is (0,-3,9);
- 2nd point: if x=3, then z=0 and y=3-2z=3-0=3, so the 2nd point is (3,0,3).
The perpendicular plane to the plane x+y-4z=6 is parallel to the vector with coordinates (1,1,-4) (normal vector of the given plane).
Hence, the equation of needed plane is
![\left\|\begin{array}{ccc}x-0&y-(-3)&z-9\\3-0&0-(-3)&3-9\\1&1&-4\end{array}\right\|=0\Rightarrow \left\|\begin{array}{ccc}x&y+3&z-9\\3&3&-6\\1&1&-4\end{array}\right\|=0](https://tex.z-dn.net/?f=%5Cleft%5C%7C%5Cbegin%7Barray%7D%7Bccc%7Dx-0%26y-%28-3%29%26z-9%5C%5C3-0%260-%28-3%29%263-9%5C%5C1%261%26-4%5Cend%7Barray%7D%5Cright%5C%7C%3D0%5CRightarrow%20%5Cleft%5C%7C%5Cbegin%7Barray%7D%7Bccc%7Dx%26y%2B3%26z-9%5C%5C3%263%26-6%5C%5C1%261%26-4%5Cend%7Barray%7D%5Cright%5C%7C%3D0)
Thus,
![\left\|\begin{array}{ccc}x&y+3&z-9\\3&3&-6\\1&1&-4\end{array}\right\|=0\Rightarrow \\\\-12x-6(y+3)+3(z-9)-3(z-9)+6x+12(y+3)=0\\ \\-6x+6(y+3)=0\\ \\-x+y+3=0\\ \\x-y-3=0](https://tex.z-dn.net/?f=%5Cleft%5C%7C%5Cbegin%7Barray%7D%7Bccc%7Dx%26y%2B3%26z-9%5C%5C3%263%26-6%5C%5C1%261%26-4%5Cend%7Barray%7D%5Cright%5C%7C%3D0%5CRightarrow%20%5C%5C%5C%5C-12x-6%28y%2B3%29%2B3%28z-9%29-3%28z-9%29%2B6x%2B12%28y%2B3%29%3D0%5C%5C%20%5C%5C-6x%2B6%28y%2B3%29%3D0%5C%5C%20%5C%5C-x%2By%2B3%3D0%5C%5C%20%5C%5Cx-y-3%3D0)